Question

A block of mass $m$ moving with velocity $v_0$ on a smooth horizontal surface hits the spring of constant $K$ as shown. The maximum compression in spring is

• A. $\sqrt{\frac{2m}{K}}{v}_0$
• B. $\sqrt{\frac{m}{K}}{v}_0$
• C. $\sqrt{\frac{m}{2K}}{v}_0$
• D. $\sqrt{\frac{m}{4K}}{v}_0$

Answer 1

The correct option is B $\sqrt{\frac{m}{K}}{v}_0$

According to law of conservation of energy
$E_i=E_f$
$U_i+K_i=U_f+K_f$
[Sum of potential energy stored in spring and kinetic energy of block will be constant]
[$U_i=0,$ as spring is unstretched]
$0+\frac{1}{2}m{v}_0^2=\frac{1}{2}K{x}^2$
[for maximum compression $K_f=0$]
$x=\sqrt{\frac{m}{K}}{v}_0$
Maximum compression in spring, $x=\sqrt{\frac{m}{K}}{v}_0$